Quality & Quantity 37: 99–110, 2003.
© 2003 Kluwer Academic Publishers. Printed in the Netherlands.
An Approximate Test for Homogeneity of
Correlated Correlation Coefﬁcients
University of Michigan
Abstract. This paper develops and evaluates an approximate procedure for testing homogeneity of
an arbitrary subset of correlation coefﬁcients among variables measured on the same set of individu-
als. The sample may have some missing data. The simple test statistic is a multiple of the variance
of Fisher r-to-z transformed correlation coefﬁcients relevant to the null hypothesis being tested and
is referred to a chi-square distribution. The use of this test is illustrated through several examples.
Given the approximate nature of the test statistics, the procedure was evaluated using a simulation
study. The accuracy in terms of the nominal and the actual signiﬁcance levels of this test for several
null hypotheses of interest were evaluated.
Key words: chisquare test, Fisher r-to-z, missing data
A common situation in social science research involves a comparison a set of
correlation coefﬁcients between variables measured on the same subjects. For
(1) In an evaluation of several instruments for scoring a certain attribute, testing
for the homogeneity of correlation coefﬁcients between scores obtained using
(2) Suppose that there are several, possibly nested instruments of differing length
(hence, differing costs) for scoring current health status and the objective is to
relate the current health status score to the medical cost or utilization. If all the
current health status scores from different instruments are equally correlated
to the dependent variable (medical costs) then the shortest instrument may be
used to reduce costs.
An important difference between these two problems is that in the former, all
possible p(p−1)/2 pairwise correlation coefﬁcients among, say p, score variables
are being tested for equality whereas in the second example only a subset of p − 1
of the p(p − 1)/2 possible pairwise correlation coefﬁcients are involved in the
null hypothesis. The means and variances are the nuisance parameters in the ﬁrst